Asymptotic quantization of exponential random graphs

Abstract

We describe the asymptotic properties of the edge-triangle exponential random graph model as the natural parameters diverge along straight lines. We show that as we continuously vary the slopes of these lines, a typical graph drawn from this model exhibits quantized behavior, jumping from one complete multipartite graph to another, and the jumps happen precisely at the normal lines of a polyhedral set with infinitely many facets. As a result, we provide a complete description of all asymptotic extremal behaviors of the model.

38 pages, 7 figures

References in corpus (4)

• Graph limits and exchangeable random graphs
• Introduction to papers on the modeling and analysis of network data
• Closures of exponential families
• Introduction to papers on the modeling and analysis of network data---II

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